How to determine the target value when using ReLU as activation function?
ReLU and sigmoid have different properties (i.e. range), as you already noticed. I've never seen the ReLU being used as the activation function of the output layer (but some people may use it for some reason, e.g. regression tasks where the output needs to be positive). ReLU is usually used as the activation function of a hidden layer. However, in your case, you don't have hidden layers.

The sigmoid function is used as the activation function of the output layer when you need to interpret the output of the neural network as a probability, i.e. a number between $0$ and $1$, given that the sigmoid function does exactly this, i.e. it squashes its input to the range $[0, 1]$, i.e. $\text{sigmoid}(x) = p \in [0, 1]$. When do you need the output of the network to be a probability?  For example, if you decide to use the cross-entropy loss function (which is equivalent to the negative log-likelihood), then the output of your network should be a probability. For example, if you need to solve a binary classification task, then the combination of a sigmoid as the activation function of the output layer and the binary cross-entropy as the loss function is probably what you need.

You could also have a classification problem with more than 2 classes (multi-class classification problem). In that case, you probably need to use a softmax as the activation function of your network combined with a cross-entropy loss function.

See this question How to choose cross-entropy loss in TensorFlow? on Stack Overflow for more info about different cross-entropy functions.

By the way, in general, the targets don't necessarily need to be restricted to be 0 or 1. For example, if you are solving a regression task, your target may just be any number. However, in that case, you may need another loss function (which is often the mean squared error).